Model and data fitting

Based on the characterized distribution of the signal and the noise, we can now simulate the final effect of the different values for these parameters and evaluate the expected result in the measurement. By doing it in the inverse order, we can estimate the values of the different parameters by trying to fit the measured result with the output model of our simulation where we can modify the mean value of the noise and signal.

Figure IV.27. Schematics of the generation and fitting of the different parameters for noise and signal.

To do so we first start from initial parameters, generate the expected distribution for the signal and noise. Then, we analyze the outcome distribution and try to fit to the measured values. The sum of the quadratic residual of every point, referred as the residual sum of squares (RSS), will be used to compare the different fittings. In the next step, a slightly different parameter is used to generate the same process and the RSS between them is compare. Based on their difference, and the change introduced in the parameters, the systems outcomes the final values for the different parameters changed in the fitting until the optimum fit with the lowest RSS is achieved.

For the sake of simplicity, we will only show a few cases of the whole range of measurements taken for the different scenarios. As we faced an enormous range of measurements we decided to modify the system to program an automatic fit in the live signal. For that purpose, we prepared new routines to implement in the system. As the whole measurement equipment was controlled by a PC motherboard with a commercial processor

Supported by the pre-installed drivers in the software, we could manage the acquisition and control of the measurement set-up.

The acquisition was performed by the same software and later in the same task the data were fitted. To do so the system controlled the TLS, set the central wavelength. After that, the signal from the detector was acquired at the maximum rate for a short period of time and saved as an array in the workspace. The software worked out the statistical analysis of the data, and proceeded to the fitting. Based on a standard minimum search algorithm, the software output the parameters that present the lowest residuals with respect to the measured data.

In figure IV.28, the systems present the statistical analysis of the registered values for different ASE levels.

Figure IV.28. Measured data and fitting curve for different values of OSNR.

In figure IV.29, we show the mean different values obtained for the different scenarios studied.

Figure IV.29. Obtained values and reference values showing the divergence for low values of ASE.

In the graph IV.29, it can be seen that for a certain range of values the system exhibits good results; however for low values of ASE it does not achieve acceptable results. For low ASE values, i.e. below -50dBm measured in a 10Mhz resolution, the systems final values deviated more than 5 dB from the reference values. Our first guess was a duplicity of minimum residual for different parameters or an inefficient minimum search algorithm that cannot get out of a local minimum. After analyzing the residual function for the values of the different parameters, we realized that even for the correct values the model could not reproduced the expected statistical behavior. So far, although it can be seen the different shape in the histograms for the different values, we have not been able to extract the real value of the underlying noise for low ASE values.

IV.7.

Conclusions

In this chapter, we have studied the use of the ultra-high resolution spectroscopy to analyze the dynamic of the instantaneous power spectral density in live signals. We have focused the research in the use of stimulated Brillouin scattering and the analysis of 10MHz wide spectral regions. We also have centered the analysis in live signals following the ITU recommendations for SDH protocol.

Throughout the chapter the main goal has been the search and study of new techniques that could be employed in those scenarios were the polarization has been used for modulation too, i.e. PolMux. This polarization multiplexing impedes the use of the polarization selective techniques as, in times longer than the bit, the signal can be considered depolarized, like the noise. In our proposal, we studied and focused on one of the remaining physical properties that might be exploited for their differentiation, the coherence.

Our starting point was the assumption that due to their different source of origin the signal and the noise present different coherence. We tested how the length of the pattern and

where short patterns were introduced in the data stream, we were able to resolve spectral components, which PSD was zero and thus the power detected would correspond to other noise sources than the signal.

Based on the regulations, we studied the constraints imposed in the construction of the final data streams to be transmitted. We identified several cases in which the protocol established short pattern repetitions for management purposes. Aided by a commercial generator we studied the spectral shape of different mappings and multiplexing depending of the origin of the signal. Later on, we developed algorithm to synthesize the final stream according to the regulations and tested with a pulse pattern generator.

The technique developed after the study relies on the statistical analysis of the optical power from the instantaneous power spectra registered for different spectral components of the signal. We redesigned the optical spectrum analysis to switch the sweeping mode to a static registering of the instantaneous PSD for narrow spectral regions over a period of time. Based on the recovered optical spectrum of the signal, the system select suitable points to perform the statistical analysis of the registered power values. By sampling these spectral regions over a brief period of time, the statistical distribution of the registered power is calculated. The statistical analysis presents different features that respond to the values of the noise. The distortion when the noise was present or not and also its modification when the noise values increase or decrease corroborates the influence stated from the theoretical analysis.

With this information, we analyzed the influence of the noise and worked out a model of interaction between them. Based on the simulated model, we generate the expected histogram for a certain value of incoherent noise in the signal, and compare with the measured values. By controlling the simulation values, we expected to fit the two histograms and thus estimate the reference ASE value from the best fit. The main goal was to monitor the noise level from the value and shape of the registered histogram.

V. Conclusions

Throughout this thesis, novel approaches for the measurement of impairments in the optical domain have been studied. Due to the advantages that the analysis in the optical domain presents, compared to the analysis in the electrical domain; the research has been focused on the analysis and identification of the inherent limitations, that the common impairments present for its measurement with all-optical techniques.

Searching for higher spectral efficiency, the new modulation schemes have been designed to code the information using the different physical properties of the electromagnetic waves. We have studied how the conveying of these physical properties in the signal affects its differentiation with the optical noise when all-optical techniques are employed. We have also presented the new challenges that the current and future monitoring techniques must address in the next generation.

In order to assess the ultimate limitations of the analysis in the optical domain, we have employed the Stimulated Brillouin Scattering as the filtering technique to resolve the spectra. Due to its high resolution and its polarization selectivity the technique recovers most of the available information that can be extracted from the optical spectrum.

In the light of the results of the work carried out throughout this thesis, the main findings and conclusions can be summarized as follows:

• The use of U-DWDM and narrow filtering harshens the measurement of OSNR based on the identification of noise and signal in the optical spectrum. In these scenarios, the resolution of the filtering technique plays a major role and thorough analysis of the measurements must be done when ROADM are employed. The SBS filtering presents great performance in this scenario due to its high resolution, although this narrow filtering comes with a reduced sensitivity that limits the measureable PSD of the noise.

• The analysis of the impairments for multicarrier modulation formats schemes cannot be performed in the optical domain with the current regulations because they were designed for singles carrier schemes. For these schemes, the use of high resolution presents additional advantages as it can characterize the quality of the modulation based on the spectra recovered.

• SBS filtering can be used to achieve an individual characterization of the subcarriers involved in MCM schemes, such as the OFDM. We developed an algorithm in order to measure and isolate the optical power values of the different subcarriers present,

relationship between these two parameters. Based on this defined SC-OSNR we managed to measure the individual performance of the different subcarriers. This characterization opens the possibility of designing schemes attending to the distortion of each sub-carrier, instead of a global averaged performance for the complete multicarrier modulation.

• When signal and noise share the same bandwidth in the spectrum, there may exist no points where the ASE can be measured. In these scenarios the different polarization properties of the noise and signal can be exploited for its differentiation. Taking advantage of the vectorial properties of the SBS, the OSNR can be resolved in-band by generating, in the signal, a selective and severe drift of the SOP of different spectral components. Without needing a polarizer and taking advantage of its high- resolution, the system can selectively suppress the signal contribution in several spectral components and reveal the underlying noise.

• By improving the polarization control of the pump in the SBS, a new method for the measurement of the SOP across the signal bandwidth has been developed. Based on the SBS spectral resolution and its polarization dependent gain we achieved a fully spectrally resolved polarimetry with the spectral resolution of the standard SBS. Without prior alignment or knowledge of the SUT, it can resolve the SOP for multiple signals in wide spans without losing the in-band resolution.

• Polarization can be used to differentiate noise and signal as long as it is not Pol-MUX. However, the depolarization nature associated with the noise can be misunderstood with the depolarization phenomena associated with PMD or non-linear effects in polarized signals. In these cases, an ordinary measurement of the degree of the polarization, or a simple projection over a linear polarizer proves to be insufficient, in order to distinguish between signal and noise according to their SOP. For these cases, the high-resolution spectrally-resolved polarimetry can obtain the full characterization of the SOP across the signal bandwidth. With this information, all the polarization impairments present in the signal can be quantified and classified according to its value and variations across the signal bandwidth.

• The polarization multiplexing schemes preclude the use of polarization nulling techniques. When the signal is modulated with two uncorrelated streams of data in two orthogonal polarization, the use of the polarization properties is no longer valid, as the outcome presents an effective depolarization, which resembles to the noise. For these cases, a novel technique is proposed. Based on the measurement of the instantaneous power spectra and its dynamic, the system can differentiate between the signal and noise components, due to the remaining correlation that exists in the modulated signal when following the communications standards. Although the measurements agree with the initial assumptions, we only succeeded in those cases

where the noise level was high and we could not measure significant values for a robust technique.

ANNEX A

References

Agrawal G.P. 2005. "Chapter 6. Optical Amplifier Noise". In Lightwave Technology:

Telecommunication Systems. John Wiley & Sons.

Agrawal G.P. 2012. Fiber-Optic Communication Systems. John Wiley & Sons.

Baney D.M., B. Szafraniec, and A. Motamedi. 2002. "Coherent Optical Spectrum Analyzer".

Ieee Photonics Technology Letters 14, no. 3 (March): 355–357.

Becker P.M., A.A. Olsson, and J.R. Simpson. 1999. Erbium-Doped Fiber Amplifiers:

Fundamentals and Technology. Academic Press.

Bononi A., A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo. 2003. "Degree of Polarization Degradation due to Cross-Phase Modulation and Its Impact on Polarization-Mode Dispersion Compensators". Journal of Lightwave Technology 21, no. 9 (September): 1903–1913.

Buchali F., W. Baumert, H. Bulow, and J. Poirrier. 2002. "A 40 Gb/s Eye Monitor and Its Application to Adaptive PMD Compensation". In Optical Fiber Communication

Bülow H., and S. Lanne. 2004. "PMD Compensation Techniques". Journal of Optical and

Fiber Communications Reports 1, no. 3 (November 1): 283–303.

Cai J.-X., M. Nissov, A.N. Pilipetskii, and N.S. Bergano. 2008. "Automatic PMD Compensation over Transoceanic Distance with Time Varying SOP, PSP, and PMD". In Conference on Optical Fiber communication/National Fiber Optic Engineers

Conference, 2008. OFC/NFOEC 2008, 1–3.

Campos J.M., A. Destrez, J. Jacquet, and Z. Toffano. 2004. "Ultra-Fast Optical Spectrum Analyzer for DWDM Applications". Ieee Transactions on Instrumentation and

Measurement 53, no. 1 (February): 124–129.

Chan C.C.K. 2010. Optical Performance Monitoring: Advanced Techniques for Next-

Generation Photonic Networks. Burlington, MA: Academic Pr Inc.

Chang R.W. 1966. "Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission". Bell System Technical Journal, The 45, no. 10 (December): 1775– 1796.

Choi H.Y., Y. Takushima, and Y.C. Chung. 2008. "OSNR Monitoring Technique for DPSK/DQPSK Signals Based on Self-Heterodyne Detection". Ieee Photonics

Technology Letters 20, no. 13-16 (August): 1124–1126.

Collett E. 2005. Field Guide to Polarization. Bellingham, Wash: SPIE Publications.

Cornick K.E., S.D. Dods, M. Boroditsky, and P.M. Farrell. 2005. "All-Order PMD Penalty Prediction Using SOP String Lengths". In , 702–703.

Cornick K.E., K. Hinton, S.D. Dods, and P.M. Farrell. 2008. "A Framework for Evaluating the System Penalty From Polarization-Mode Dispersion Using Different Performance Monitoring Techniques". Journal of Lightwave Technology 26, no. 13 (July): 1790–1797.

Dahan D., U. Mahlab, A. Teixeira, I. Zacharopoulos, and I. Tomkos. 2011. "Optical Performance Monitoring for Translucent/transparent Optical Networks RID D- 6304-2011". Iet Optoelectronics 5, no. 1 (February): 1–18.

Derickson D. 1997. Fiber Optic Test and Measurement. 1 edition. Upper Saddle River, N.J: Prentice Hall.

Van Deventer M.O., and A.J. Boot. 1994. "Polarization Properties of Stimulated Brillouin Scattering in Single-Mode Fibers". Journal of Lightwave Technology 12, no. 4 (April): 585–590.

Fabrega J.M., M.S. Moreolo, M. Chochol, and G. Junyent. 2013. "Impact of Modulator Driving on Constant Envelope Optical OFDM Based on Hartley Transform". IEEE

FERREIRA M.F., A.N. PINTO, P.S. ANDRÉ, N.J. MUGA, J.E. MACHADO, R.N. NOGUEIRA, S.V. LATAS, M.H. SOUSA, and J.F. ROCHA. 2005. "Polarization Mode Dispersion in High-Speed Optical Communication Systems". Fiber and

Integrated Optics 24, no. 3-4 (May 1): 261–285.

Gordon J., and H. Kogelnik. 2000. "PMD Fundamentals: Polarization Mode Dispersion in Optical Fibers". PROCEEDINGS OF THE NATIONAL ACADEMY OF

SCIENCES OF THE UNITED STATES OF AMERICA 97, no. 9 (April 25): 4541–

4550.

Govind P. A. 2006a. Nonlinear Fiber Optics. Fourth. San Diego: Academic Press.

Govind P. A. 2006b. "Chapter 9 - Stimulated Brillouin Scattering". In Nonlinear Fiber Optics

(Fourth Edition), 329–367. San Diego: Academic Press.

Gumaste A., and T. Antony. 2003. DWDM Network Designs and Engineering Solutions. Cisco Press.

Heras C., J.M. Subias, J. Pelayo, and F. Villuendas. 2007. "Polarization Properties of Optical Spectral Components Generated by XPM Effect". Journal of Lightwave Technology 25, no. 5 (May): 1313–1321.

Hill G., P. Chidgey, F. Kaufhold, T. Lynch, O. Sahlen, M. Gustavsson, M. Janson, et al. 1993. "A Transport Network Layer Based on Optical Network Elements". Journal of

Lightwave Technology 11, no. 5-6 (June): 667–679.

Hobbs P.C.D. 2011. Building Electro-Optical Systems: Making It All Work. John Wiley & Sons.

IEC. 1992. IEC 61280-2-9:2009. Fibre Optic Communication Subsystem Test Procedures -

Part 2-9: Digital Systems - Optical Signal-to-Noise Ratio Measurement for Dense Wavelength-Division Multiplexed Systems.

ITU-T. 2004. G.697 : Optical Monitoring for DWDM Systems.

ITU-T. 2007. G.650.2.Definitions and Test Methods for Statistical and Non-Linear Related

Attributes of Single-Mode Fibre and Cable.

ITU-T. 2012. G.694.1 : Spectral Grids for WDM Applications: DWDM Frequency Grid. Jose Martinez J., A. Villafranca, C.D. Heras, M.I. Roche, J.M. Subias, J. Pelayo, E. Pellejer,

P. Blasco, and J.I. Garces. 2010. "In-Band Optical Signal-to-Noise Ratio Monitoring Method Based on High-Resolution Polarization Analysis and Induced Differential Group Delay". Applied Optics 49, no. 32 (November 10): 6213–6216.

Kao K.C., and G.A. Hockham. 1966. "Dielectric-Fibre Surface Waveguides for Optical Frequencies". Proceedings of the Institution of Electrical Engineers 113, no. 7: 1151.

Keiser G. 2010. Optical Fiber Communications. 4 edition. New York, NY: McGraw-Hill Science/Engineering/Math.

Kilper D.C., S. Chandrasekhar, L. Buhl, A. Agarwal, and D. Maywar. 2002. "Spectral Monitoring of OSNR in High-Speed Networks". In 28th European Conference on

Optical Communication, 2002. ECOC 2002, 3:1–2.

Lachs G. 1998. Fiber Optics Communications. 1 edition. New York: McGraw-Hill Professional.

Lee J.H., D.K. Jung, C.H. Kim, and Y.C. Chung. 2001. "OSNR Monitoring Technique Using Polarization-Nulling Method". Ieee Photonics Technology Letters 13, no. 1 (January): 88–90.

Lee J.H., N. Yoshikane, T. Tsuritani, and T. Otani. 2008. "In-Band OSNR Monitoring Technique Based on Link-by-Link Estimation for Dynamic Transparent Optical Networks". Journal of Lightwave Technology 26, no. 9-12 (June): 1217–1225. Liu X., Y.-H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, and L.L. Buhl. 2007. "OSNR

Monitoring Method for OOK and DPSK Based on Optical Delay Interferometer".

Ieee Photonics Technology Letters 19, no. 13-16 (August): 1172–1174.

Luis R.S., A. Teixeira, and P. Monteiro. 2009. "Optical Signal-to-Noise Ratio Estimation Using Reference Asynchronous Histograms". Journal of Lightwave Technology 27, no. 5-8 (April): 731–743.

Luo T., C.Y. Yu, Z.Q. Pan, Y. Wang, Y. Arieli, and A.E. Willner. 2005. "Dispersive Effects Monitoring for RZ Data by Adding a Frequency-Shifted Carrier along the Orthogonal Polarization State". Journal of Lightwave Technology 23, no. 10 (October): 3295–3301.

MICIN. 2010. TEC2010-17869 Monitorización de Las Prestaciones Ópticas de Redes de Nueva

Generación.

Moller L., and L. Buhl. 2001. "Method for PMD Vector Monitoring in Picosecond Pulse Transmission Systems". JOURNAL OF LIGHTWAVE TECHNOLOGY 19, no. 8 (August): 1125–1129.

National Semiconductor. 1980. "Power Spectra Estimation". Application Note 255. http://archive.org/details/bitsavers_nationalap_328213.

Nezam S.M.R., J.E. McGeehan, and A.E. Willner. 2004. "Theoretical and Experimental Analysis of the Dependence of a Signal’s Degree of Polarization on the Optical-Data Spectrum". Journal of Lightwave Technology 22, no. 3 (March): 763–772.

Ohteru S., and N. Takachio. 1999. "Optical Signal Quality Monitor Using Direct Q-Factor Measurement". IEEE Photonics Technology Letters 11, no. 10 (October): 1307–1309.

Pelayo Z.F.J., E.R. Alonso, H.P. Blasco, G.J.I. Garces, V.C. Heras, T.F.M. Lopez, D.J. Subias, and Y.F. Villuendas. 2004. "Dispositivo Analizador de Espectros Opticos Por Difusion Brillouin Y Procedimiento de Medida Asociado".

Proakis J.G. 2001. Digital Communications. McGraw-Hill.

Rogers A. 2008. Polarization in Optical Fibers. Norwood, MA: Artech House.

Roudas I., G. Piech, M. Mlejnek, Y. Mauro, D. Chowdhury, and M. Vasilyev. 2004. "Coherent Frequency-Selective Polarimeter for Polarization-Mode Dispersion Monitoring". JOURNAL OF LIGHTWAVE TECHNOLOGY 22, no. 4 (April): 953–967.

Saleh A.A.M., and J.M. Simmons. 2006. "Evolution Toward the Next-Generation Core Optical Network". Journal of Lightwave Technology 24, no. 9 (September 3): 3303. Schonfelder T., and DE. 2003. "United States Patent: 6580535 - Polarization Division

Multiplexing in Optical Data Transmission Systems".

Sevillano P., J. Subias, Z. Pelayo, V. Heras, V. Villafranca, and T. Lopez. 2014. "System and Method for Measuring a Wavelength-Resolved State of Polarization of an Optical Signal".

Shake I., W. Takara, S. Kawanishi, and Y. Yamabayashi. 1998. "Optical Signal Quality Monitoring Method Based on Optical Sampling". Electronics Letters 34, no. 22 (October 29): 2152–2154.

Shieh W., and C. Athaudage. 2006. "Coherent Optical Orthogonal Frequency Division Multiplexing". Electronics Letters 42, no. 10 (May 11): 587–589.

Subías J., J. Pelayo, F. Villuendas, C. Heras, and E. Pellejer. 2005. "Very High Resolution Optical Spectrometry by Stimulated Brillouin Scattering". Ieee Photonics Technology

Letters 17, no. 4 (April): 855–857.

Tomkos I., M. Angelou, R.J.D. Barroso, I. de Miguel, R.M.L. Toledo, D. Siracusa, E. Salvadori, A. Tymecki, Y. Ye, and I.T. Monroy. 2012. "Next Generation Flexible and Cognitive Heterogeneous Optical Networks". In The Future Internet, ed. F. Álvarez, F. Cleary, P. Daras, J. Domingue, A. Galis, A. Garcia, A. Gavras, et al., 225– 236. Lecture Notes in Computer Science 7281. Springer Berlin Heidelberg.

Vandeventer M., C. Deblok, and C. Park. 1991. "High-Dynamic-Range Heterodyne Measurement of Optical-Spectra". Optics Letters 16, no. 9 (May 1): 678–680. Villafranca A. 2008. "Development of Brillouin Optical Spectroscopy Techniques and